ROME—Greek Finance Minister Yanis Varoufakis said Greece needs “a bridge agreement” on its debt situation that could in turn lead to a full accord by June.

Greece’s new Prime Minister Alexis Tsipras and Mr. Varoufakis are touring European capitals in an effort to persuade fellow European leaders to reverse the stringent terms of Greece’s €240 billion ($272 billion) bailout.

“What...

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